Mastering Python for Finance

Python is free in terms of license. Documentation is widely available, and many Python online community groups are available, where one can turn in times of doubt. Because it is free and open source, anyone can easily view or modify the algorithms in order to adapt to customized solutions.

Being accessible to the public opens a whole new level of opportunities. Anyone can contribute existing enhancements or create new modules. For advanced users, interoperability between different programming languages is supported. A Python interpreter may be embedded in C and C++ programs. Likewise, with the appropriate libraries, Python may be integrated with other languages not limited to Fortran, Lisp, PHP, Lua, and more.

Python is available on all major operating systems, such as Windows, Unix, OS/2, Mac, among others.

Python as a general-purpose, high-level programming language allows the user to focus on problem solving and leave low-level mechanical constructs such as memory management out of the picture.

The expressiveness of the Python programming language syntax helps quantitative developers in implementing prototypes quickly.

Python allows the use of object-oriented, procedural, as well as functional programming styles. Because of this flexibility, it is especially useful in implementing complex mathematical models containing multiple changeable parameters.

By now, you should be familiar with the NumPy, SciPy, matplotlib, statsmodels, and pandas modules, as indispensable tools in quantitative analysis and data management.

Other libraries extend the functionalities of Python. For example, one may turn Python into a data visualization tool with the gnuplot package in visualizing mathematical functions and data interactively. With Tk-based GUI tools such as Tkinter, it is possible to turn Python scripts into GUI programs.

A widely popular shell for Python is IPython, which provides interactive computing and high-performance tools for parallel and distributed computing. With IPython Notebook, the rich text web interface of IPython, you can share code, text, mathematical expressions, plots, and other rich media with your target audience. IPython was originally intended for scientists to work with Python and data.

As the demand for clarity, speed, and flexibility in your program increases, it is important to keep your code readable, manageable, and lean. One popular technical approach to building software systems is by applying the object-oriented paradigm. Consider the following example of displaying a greeting message as a class:

class Greeting(object):

    def __init__(self, my_greeting):
        self.my_greeting = my_greeting

    def say_hello(self, name):
        print "%s %s" % (self.my_greeting, name)

We created a class called Greeting that is capable of accepting an input argument in its constructor. For this example, we will define our greeting as "Hello". The say_hello function is invoked with an input name and prints our greeting messages as follows:

>>> greeting = Greeting("Hello")
>>> greeting.say_hello("World")
>>> greeting.say_hello("Dog")
>>> greeting.say_hello("Cat")
Hello World
Hello Dog
Hello Cat

We can achieve the same Greeting functionality using the functional approach. Functional programming is a programming paradigm, where computer programs are structured and styled in such a way that they can be evaluated as mathematical functions. These pseudo mathematical functions avoid changing state data, while increasing reusability and brevity.

In Python, a function object can be assigned to a variable and, like any other variables, can be passed into functions as an argument as well as return its value.

Let's take a look at the following code that gives us the same output:

from functools import partial
def greeting(my_greeting, name):
    print "%s %s" % (my_greeting, name)

Here, we defined a function named greeting that takes in two arguments. Using the partial function of the functools module, we treated the function, greeting, as an input variable, along with our variable greeting message as Hello.

>>> say_hello_to = partial(greeting, "Hello")
>>> say_hello_to("World")
>>> say_hello_to("Dog")
>>> say_hello_to("Cat")

We assigned the say_hello_to variable as its return value, and reused this variable in printing our greetings with three different names by executing it as a function that accepts input arguments.

There is no clear answer to this question. We have just demonstrated that Python supports both the object-oriented approach and the functional approach. We can see that in certain circumstances the functional approach in software development is brevity to a large extent. Using the say_hello_to function provides better readability over greeting.say_hello(). It boils down to the programmer's decision as to what works best in making the code more readable and having ease of maintenance during the software life cycle while collaborating with fellow developers.

As a general rule of thumb, in large and complex software systems representing objects as classes helps in code management between team members. By working with classes, the scope of work can be more easily defined, and system requirements can be easily scaled using object-oriented design. When working with financial mathematical models, using functional programing helps to keep the code working in the same fashion as its accompanying mathematical concepts.

Depending on how you have installed Python on your machine, IPython might have been included in your Python environment. Please consult the IPython official documentation for the various installation methods most comfortable for you. The official page is available at http://ipython.org.

IPython can be downloaded from https://github.com/ipython. To install IPython, unpack the packages to a folder. From the terminal, navigate to the top-level source directory and run the following command:

$ python setup.py install

The pip tool is a great way to install Python packages automatically. Think of it as a package manager for Python. For example, to install IPython without having to download all the source files, just run the following command in the terminal:

$ pip install ipython

To get pip to work in the terminal, it has to be installed as a Python module. Instructions for downloading and installing pip can be found at https://pypi.python.org/pypi/pip.

The IPython Notebook is the web-based interactive computing interface of IPython used for the whole computation process of developing, documenting, and executing the code. This section covers some of the common features in IPython Notebook that you may consider using for building financial applications.

Here is a screenshot of the IPython Notebook in Windows OS:

Notebooks allow in-browser editing and executing of the code with the outputs attached to the code that generated them. It has the capability of displaying rich media, including images, videos, and HTML components.

Its in-browser editor allows the Markdown language that can provide rich text and commentary for the code.

Mathematical notations can be included with the use of LaTeX, rendered natively by MathJax. With the ability to import Python modules, publication-quality figures can be included inline and rendered using the matplotlib library.

$ ipython notebook

Creating a new notebook

Click on New Notebook from the dashboard to create a new notebook. You can navigate to the File | New menu option from within an active notebook:

Here, you will be presented with the notebook name, a menu bar, a toolbar, and an empty code cell.

The menu bar presents different options that may be used to manipulate the way the notebook functions.

The toolbar provides shortcuts to frequently used notebook operations in the form of icons.

Each logical section in a notebook is known as a cell. A cell is a multi-line text input field that accepts plain text. A single notebook document contains at least one cell and can have multiple cells.

To execute the contents of a cell, from the menu bar, go to Cell | Run, or click on the Play button from the toolbar, or use the keyboard shortcut Shift + Enter.

Each cell can be formatted as a Code, Markdown, Raw NBConvert, or heading cell:

Let's get started by creating a new notebook and populating it with some content. We will insert the various types of objects to demonstrate the various tasks.

Creating a notebook with heading and Markdown cells

We will begin by creating a new notebook by performing the following steps:

1. Click on New Notebook from the dashboard to create a new notebook. If from within an active notebook, navigate to the File | New menu option.

2. In the input field of the first cell, enter a page title for this notebook. In this example, type in Welcome to Hello World.

3. From the options toolbar menu, go to Cells | Cell Type and select Heading 1. This will format the text we have entered as the page title. The changes, however, will not be immediate at this time.

4. From the options toolbar menu, go to Insert | Insert Cell Below. This will create another input cell below our current cell.

5. In this example, we will insert the following piece of text that contains the Markdown code:

   Text Examples
   ===
   
   This is an example of an *italic* text.
   
   This is an example of a **bold*** text.
   
   This is an example of a list item:
   - Item #1
   - Item #2
   - Item #3
   
   ---
   
   #heading 1
   ##heading 2
   ###heading 3
   ####heading 4
   #####heading 5
   ######heading 6

6. From the toolbar, select Markdown instead of Code.

7. To run your code, go to Cell | Run All. This option will run all the Python commands and format your cells as required.

   Tip

   When the current cell is executed successfully, the notebook will focus on the next cell below, ready for your next input. If no cell is available, one will be automatically created and will receive the input focus.

This will give us the following output:

Mathematical operations in cells

Let's perform a simple mathematical calculation in the notebook; let's add the numbers 3 and 5 and assign the result to the answer variable by typing in the code cell:

answer = 3 + 5

From the options menu, go to Insert | Insert Cell Below to add a new code cell at the bottom. We want to output the result by typing in the following code in the next cell:

print answer

Next, go to Cell | Run All. Our answer is printed right below the current cell.

Displaying graphs

The matplotlib module provides a MATLAB-like plotting framework in Python. With the matplotlib.pyplot function, charts can be plotted and rendered as graphic images for display in a web browser.

Let's demonstrate a simple plotting functionality of the IPython Notebook. In a new cell, paste the following code:

import numpy as np
import math
import matplotlib.pyplot as plt

x = np.linspace(0, 2*math.pi) 
plt.plot(x, np.sin(x), label=r'$\sin(x)$') 
plt.plot(x, np.cos(x), 'ro', label=r'$\cos(x)$') 
plt.title(r'Two plots in a graph') 
plt.legend() 

The first three lines of the code contain the required import statements. Note that the NumPy, math, and matplotlib packages are required for the code to work in the IPython Notebook.

In the next statement, the variable x represents our x axis values from 0 through 7 in real numbers. The following statement plots the sine function for every value of x. The next plot command plots the cosine function for every value of x as a dotted line. The last two lines of the code print the title and legend respectively.

Running this cell gives us the following output:

Inserting equations

What is TeX and LaTeX? TeX is the industry standard document markup language for math markup commands. LaTeX is a variant of TeX that separates the document structure from the content.

Mathematical equations can be displayed using LaTeX in the Markdown parser. The IPython Notebook uses MathJax to render LaTeX surrounded with $$ inside Markdown.

For this example, we will display a standard normal cumulative distribution function by typing in the following command in the cell:

$$N(x) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{x} e^{- \frac{z^2}{2}}\, dz$$

Select Markdown from the toolbar and run the current cell. This will transform the current cell into its respective equation output:

Besides using the MathJax typesetting, another way of displaying the same equation is using the math function of the IPython display module, as follows:

from IPython.display import Math
Math(r'N(x) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{x} e^{- \frac{z^2}{2}}\, dz')

The preceding code will display the same equation, as shown in the following screenshot:

Notice that, since this cell is run as a normal code cell, the output equation is displayed immediately below the code cell.

We can also display equations inline with text. For example, we will use the following code with a single $ wrapping around the LaTeX expression:

This expression $\sqrt{3x-1}+(1+x)^2$ is an example of a TeX inline equation

Run this cell as the Markdown cell. This will transform the current cell into the following:

Displaying images

To work with images, such as JPEG and PNG, use the Image class of the IPython display module. Run the following code to display a sample image:

from IPython.display import Image
Image(url='http://python.org/images/python-logo.gif')

On running the code cell, it will display the following output:

Inserting YouTube videos

The lib.display module of the IPython package contains a YouTubeVideo function, where you can embed videos hosted externally on YouTube into your notebook. For example, run the following code:

from IPython.lib.display import YouTubeVideo

# An introduction to Python by Google.
YouTubeVideo('tKTZoB2Vjuk')  

The video will be displayed below the code, as shown in the following screenshot:

Working with HTML

Notebook allows HTML representations to be displayed. One common use of HTML is the ability to display data with tables. The following code outputs a table with two columns and three rows, including a header row:

from IPython.display import HTML
table = """<table>
<tr>
<th>Header 1</th>
<th>Header 2</th>
</tr>
<tr>
<td>row 1, cell 1</td>
<td>row 1, cell 2</td>
</tr>
<tr>
<td>row 2, cell 1</td>
<td>row 2, cell 2</td>
</tr>
</table>"""
HTML(table)

The HTML function will render HTML tags as a string in its input argument. We can see the final output as follows:

The pandas DataFrame object as an HTML table

In a notebook, pandas allow DataFrame objects to be represented as HTML tables.

In this example, we will retrieve the stock market data from Yahoo! Finance and store them in a pandas DataFrame object with the help of the panas.io.data.web.DataReader function. Let's use the AAPL ticker symbol as the first argument, yahoo as its second argument, the start date of the market data as the third argument, and the end date as the last argument:

import pandas.io.data as web
import datetime

start = datetime.datetime(2014, 1, 1)
end = datetime.datetime(2014, 12, 31)
df = web.DataReader("AAPL", 'yahoo', start, end)
df.head()

With the df.head() command, the first five rows of the DataFrame object that contains the market data is displayed as an HTML table in the notebook:

You are now ready to place your code in a chronological order and present the key financial information, such as plots and data to your audience. Many industry practitioners use the IPython Notebook as their preferred editor for financial model development in helping them to visualize data better.

You are strongly encouraged to explore the powerful features the IPython Notebook has to offer that best suit your modeling needs. A gallery of interesting notebook projects used in scientific computing can be found at https://github.com/ipython/ipython/wiki/A-gallery-of-interesting-IPython-Notebooks.